Investment Theory and Risk Management, + Website

Infinite Cash Flow Streams (Perpetuities)

Defined benefit pensions are perpetuities; they are like a bond with a coupon paid indefinitely (until death). A perpetuity's cash flows have to be discounted at r into the infinite future. Assuming annual payments, this is represented by:

Solving this power series yields

See Appendix 2.1 for the complete derivation. Therefore, a bond paying a $10 coupon in perpetuity with interest rate of 10 percent is worth $100. We sometimes see this written in yield form as . Yield is a very general concept in finance and one you should familiarize yourself with. For example, if a commercial property lease generates $1 million in revenues every year and you can buy this property for $20 million, then you buy the right to receive these cash flows, which have a yield of 5 percent. You can compare this yield to other asset class yields of comparable risk.